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JEE Main 2012Offline
Exam
JEE Main
Year
2012
Mode
Offline
Subject
Mathematics
Chapter
Circle

JEE Main 2012 · Offline · Mathematics · Circle

The length of the diameter of the circle which touches the x -axis...

The length of the diameter of the circle which touches the xx-axis at the point (1,0)(1,0) and passes through the point (2,3)(2,3) isThe length of the diameter of the circle which touches the x -axis at the point (1,0) and passes through the point

Options

  1. A103\frac{10}{3}
  2. B35\frac{3}{5}
  3. C65\frac{6}{5}
  4. D53\frac{5}{3}

Correct answer

A. 103\frac{10}{3}

Step-by-step solution

Let (h,k)(h, k) be centre. (h−1)2+(k−0)2=k2⇒h=1(h−2)2+(k−3)2=k2⇒k=53\begin{array}{ll} (h-1)^2+(k-0)^2=k^2 & \Rightarrow h=1 \\ (h-2)^2+(k-3)^2=k^2 & \Rightarrow k=\frac{5}{3} \end{array} ∴\therefore diameter is 2k=1032 \mathrm{k}=\frac{10}{3} The length of the diameter of the circle which touches the x -axis at the point (1,0) and passes through the point
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